Geometric Algebra for Computer Graphics

Author: John Vince

Publisher: Springer Science & Business Media

ISBN: 1846289963

Category: Computers

Page: 256

View: 2433

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Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.
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Geometric Algebra for Computer Science

An Object-Oriented Approach to Geometry

Author: Leo Dorst,Daniel Fontijne,Stephen Mann

Publisher: Elsevier

ISBN: 0080553109

Category: Computers

Page: 664

View: 2679

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Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
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Geometric Algebra: An Algebraic System for Computer Games and Animation

Author: John A. Vince

Publisher: Springer Science & Business Media

ISBN: 9781848823792

Category: Computers

Page: 195

View: 6615

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Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs. The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.
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Geometric Algebra for Computer Science (Revised Edition)

An Object-Oriented Approach to Geometry

Author: Leo Dorst,Daniel Fontijne,Stephen Mann

Publisher: Morgan Kaufmann

ISBN: 0080958796

Category: Computers

Page: 664

View: 4353

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Geometric Algebra for Computer Science (Revised Edition) presents a compelling alternative to the limitations of linear algebra. Geometric algebra (GA) is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. It systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. It covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Numerous drills and programming exercises are helpful for both students and practitioners. A companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book; and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter. The book will be of interest to professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. It is also be ideal for students in graduate or advanced undergraduate programs in computer science. Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Presents effective approaches to making GA an integral part of your programming. Includes numerous drills and programming exercises helpful for both students and practitioners. Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.
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Mathematics for Computer Graphics

Author: John A. Vince

Publisher: Springer Science & Business Media

ISBN: 9781849960236

Category: Computers

Page: 293

View: 1902

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John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry. Plus – and unusually in a student textbook – a chapter on geometric algebra is included.
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Understanding Geometric Algebra

Hamilton, Grassmann, and Clifford for Computer Vision and Graphics

Author: Kenichi Kanatani

Publisher: CRC Press

ISBN: 1482259516

Category: Computers

Page: 208

View: 7791

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Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer graphics and computer vision.Unlike similar texts
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Computer Algebra and Geometric Algebra with Applications

6th International Workshop, IWMM 2004, Shanghai, China, May 19-21, 2004 and International Workshop, GIAE 2004, Xian, China, May 24-28, 2004.Revised Selected Papers

Author: Hongbo Li,Peter J. Olver

Publisher: Springer Science & Business Media

ISBN: 9783540262961

Category: Computers

Page: 447

View: 2632

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This book constitutes the thoroughly refereed joint post-proceedings of the 6th International Workshop on Mathematics Mechanization, IWMM 2004, held in Shanghai, China in May 2004 and the International Workshop on Geometric Invariance and Applications in Engineering, GIAE 2004, held in Xian, China in May 2004. The 30 revised full papers presented were rigorously reviewed and selected from 65 presentations given at the two workshops. The papers are devoted to topics such as applications of computer algebra in celestial and engineering multibody systems, differential equations, computer vision, computer graphics, and the theory and applications of geometric algebra in geometric reasoning, robot vision, and computer graphics.
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Foundations of Geometric Algebra Computing

Author: Dietmar Hildenbrand

Publisher: Springer Science & Business Media

ISBN: 3642317944

Category: Computers

Page: 196

View: 1875

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The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
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Mathematics for Computer Graphics

Author: John Vince

Publisher: Springer Science & Business Media

ISBN: 1447162900

Category: Computers

Page: 391

View: 5067

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John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD and other areas of computer graphics in this updated and expanded fourth edition. The first four chapters revise number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, transforms, interpolation, 3D curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, and the last two chapters provide an introduction to differential and integral calculus, with an emphasis on geometry. Mathematics for Computer Graphics covers all of the key areas of the subject, including: Number sets Algebra Trigonometry Coordinate systems Transforms Quaternions Interpolation Curves and surfaces Analytic geometry Barycentric coordinates Geometric algebra Differential calculus Integral calculus This fourth edition contains over 120 worked examples and over 270 illustrations, which are central to the author’s descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics, giving a fascinating insight into the design of computer graphics software and setting the scene for further reading of more advanced books and technical research papers.
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Advances in Computer Graphics

36th Computer Graphics International Conference, CGI 2019, Calgary, AB, Canada, June 17–20, 2019, Proceedings

Author: Marina Gavrilova,Jian Chang,Nadia Magnenat Thalmann,Eckhard Hitzer,Hiroshi Ishikawa

Publisher: Springer

ISBN: 3030225143

Category:

Page: 587

View: 8659

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This book constitutes the refereed proceedings of the 36th Computer Graphics International Conference, CGI 2019, held in Calgary, AB, Canada, in June 2019. The 30 revised full papers presented together with 28 short papers were carefully reviewed and selected from 231 submissions. The papers address topics such as: 3D reconstruction and rendering, virtual reality and augmented reality, computer animation, geometric modelling, geometric computing, shape and surface modelling, visual analytics, image processing, pattern recognition, motion planning, gait and activity biometric recognition, machine learning for graphics and applications in security, smart electronics, autonomous navigation systems, robotics, geographical information systems, and medicine and art.
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